As it turns out, the dictionary is of precious little assistance with answering questions like this. I consulted a number of different dictionaries, and got a number of different answers--one said an orgy is five or more people having sex, one said more than two, one said an event dominated by "excessive" sexual activity (whatever the hell that means), and so on.
Now, to me, three people having sex is a threesome; four people having sex is a foursome; it doesn't get to be an orgy until you've got five or more people.
But is a play party an orgy? Clearly not all orgies are play parties, but is a play party an orgy? What about a play party where people aren't having penetrative sex? How about a mutual masturbation event...is that an orgy? My impulse is to say "no;" it isn't an orgy unless there are five or more people and there's fucking going on, so mutual masturbation doesn't count. (Edit: There are many kinds of sexual activities that aren't penetrative sex that I would consider to be an orgy, so I'm still not quite sure exactly where the borderline for the definition of "orgy" is.)
From there it was a short intellectual hop to wondering how many different kinds of group sex there are1, and what the relationship between them is.
So I started working on a Venn diagram of group sex. Then I started enlisting the help of all the people around me.
Then I started realizing that some of the potential overlaps are complicated beyond what you might at first think. For example, not all swing parties include group sex, yet most folks would probably think of a swing party as a group sex event.
And it soon became clear that certain rules of geometry2 precluded doing this as a traditional Venn diagram, because it's not possible to show all the overlaps and exclusions with circles.
So the project got a little more complex.
Anyway, here's what I came up with: Where group sex intersects with information theory!
Some assumptions I've made for this chart:
1. An orgy must involve penetrative sex of some kind (including manual sex) but can not involve all the participants being sexual with one and only one person; a gang bang and an orgy are exclusive, non-overlapping sex.
2. An orgy can never bee a threesome or a foursome.
3. If penetrative sex happens, it is no longer a puppy pile; ergo, orgies and gang bangs exclude puppy piles.
I have the feeling I missed some categories of group sex, though, and I don't know how universal these assumptions are.
1 As opposed to how many different kinds of sexual activity you can have in a group sex situation, which is a completely different question altogether.
2 Specifically, group theory, about which I know less than what would fit in the white space of a postage stamp.